Yes
yes

ABSTRACT

A NOVEL METHOD IS DISCLOSED FOR SOLVING THE EQUATION A(T,X)Y=EN=COL (0,0,...,0,1) FOR VARIOUS VALUES TO T, AND, FOR EACH T, FOR MANY DISTINCT VALUES OF X, AND WHEREIN, THERE IS COMBINED THE STORAGE ADVANTAGES OF THE &#34;LOOPING, PRE-INDEXED FILL&#34; TECHNIQUE WITH THE INHERENT SPEED AND STORAGE ADVANTAGES OF THE 1-2-3 GNSO TECHNIQUE FOR OBTAINING A MINIMUM STORAGE, MEDIUM SPEED ALGORITHM FOR SOLVING THE ABOVE EQUATION. THE METHOD DEFINES A NEW TYPE OF DECOMPOSITION OF THE GAUSS ELIMINATION MATRIX, G(A) OF A GIVEN MATRIX A(X,T) INTO &#34;PARTIAL&#34; GAUSS ELIMINATION OF DISTINCT MATRICES T(T) AND X(X,T), WHEREIN T CONTAINS THE NECESSARY AND SUFFICIENT DATA STRUCTURE FOR T-TYPE OPERATIONS IN G(A), I.E., T CONTAINS ONLY NONZERO ELEMENTS WHICH ARE USED IN WHOLLY T-TYPE OPERATIONS IN G(A), AND X CONTAINS THE NECESSARY AND SUFFICIENT DATA STRUCTURE FOR THE X-TYPE OPERATIONS. IN ADDITION, THE METHOD DEFINES ALGORITHMS FOR THE TWO DISTINCT PARTIAL GAUSS ELIMINATIONS G1(T,A) AND G2(X,A), EMPLOYING A LOOPING PRE-INDEXED, VARIABLITY TYPED FILL TECHNIQUE, THE METHOD ELIMINATES THE NECESSITY FOR PRECOMPILING, I.E., GENERATING AND STORING INSTRUCTIONS FOR TYPE-DECOMPOSED GAUSS ELIMINATION OF THE 1-2-3 GNSO APPROACH, AND EXTENDS IMMEDIATELY TO THE CASE OF THREE OR MORE DISTINCT   VARIABILITY TYPES APPEARING AS ARGUMENTS IN THE COEFFICIENTS OF THE MATRIX A.

DEFENSIVE PUBLICATION UNITED STATES PATENT OFFICE Published at the request of the applicant or owner in accordance with the Notice of Dec. 16. 1969, 869 O.G. 687. The abstracts of Defensive Publication applications are identified by distinctly numbered series and are arranged chronologically. The heading of each abstract indicates the number of pages of specification, including claims and sheets of drawings contained in the application as originally filed. The files of these applications are available to the public for inspection and reproduction may be purchased for 30 cents a sheet.

Defensive Publication applications have not been examined as to the merits of alleged invention. The Patent Oflice makes no assertion as to the novelty of the disclosed subject matter.

PUBLISHED OCTOBER 9, 1973 10 METHOD FOR EFFECTING GAUSS ELIMINATION X IN SPARSE MATRIX TECHNIQUES Fred G. Gustavson and Gary D. Hachtel, Ossining, N.Y.,

assignors to International Business Machines Corpora- PERFORM ORDEMNG 12 tion Armonk N.Y. FiledApr. 1973, Ser. No 348,833 BASED ON WEIGHTED OPERATION COUNT Int. Cl. G06f 7/38 US. Cl. 444-1 3 Sheets a 32 Pages Specification OOMPUTE VA=V(G(A)) AND DA-D(O(A)) H4 A novel method is disclosed for solving the equation 1 A[t,x]y=e =col (0,0, ,0,1) for various values of t, and, for each I, for many distinct values of x, and wherei i in, there is combined the storage advantages of the looping, pro-indexed fill technique with the inherent speed S'Q J QKjg'i i and storage advantages of the 1-2-3 GNSO technique for obtaining a minimum storage, medium speed algorithm for solving the above equation. The method defines a new type of decomposition of the Gauss elimination matrix, G(A) of a given matrix A(x,t) into partial Gauss elimination of distinct matrices T(t) and X(x,t), wherein T contains the necessary and sufiicient data structure for t-type operations in G(A), i.e., T contains only non- START oop BY v u mc zero elements which are used in wholly t-type operations X(x,t)-(VA-2)*A+(DA-2)*G (T,A) in G(A), and X contains the necessary and sufficient data structure for the x-type operations. In addition, the method defines algorithms for the two distinct partial Gauss eliminations G (T,A) and G (X,A), employing a looping pro-indexed, variability typed fill technique. The method eliminates the necessity for precompiling, i.e., generating and storing instructions for type-decomposed Gauss elimination of the 1-2-3 GNSO approach, and extends irnmediately to the case of three or more distinct variability types appearing as arguments in the coeflicients of the matrix A.

Oct. 9, 1973 F. G. GUSTAVSQN ET L T915303 METHOD FOR EFFECTING GAUSS ELIMINATION IN SPARSE MATRIX TECHNIQUES Filed April 6, 1975 3 Sheets-Sheet l FIG.1

INITIALIZE x AND L -10 PERFORM ORDERING BASED ON WEIGHTED OPERATION COUNT OOMPUTE VA=V(G(A)) AND DA=D(G(A)) 14 START t-LOOP BY EVALUATING T(t)=(V(A)=1)-*A CALCULATE GT=G1(T,A) 18 START X-LOOP BY EVALUATING X(X,)=(VA=2)*A+(DA-2)*G1(T,A)

CALCULATE GX= G2(X,A) 22 LAST X FOR THIS I 24 YES NO IF LAST t,STOP UPDATE x UPDATE t 28 

